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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Indecomposable decompositions and the minimal direct summand containing the nilpotents

Author: G. F. Birkenmeier
Journal: Proc. Amer. Math. Soc. 73 (1979), 11-14
MSC: Primary 16A32
MathSciNet review: 512048
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Abstract: It is well known that an indecomposable right ideal decomposition of a ring is not necessarily unique. In this paper we show that the reduced right ideals of such a decomposition are unique up to isomorphism and the remainder of the decomposition forms the unique MDSN. In the main theorem we use triangular matrices to prove that a ring with an indecomposable decomposition is basically composed of a nilpotent ring, a ring (containing a unity) with an indecomposable decomposition which equals its MDSN, and a direct sum of indecomposable reduced rings with unity.

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Keywords: Nilpotent elements, reduced ring
Article copyright: © Copyright 1979 American Mathematical Society

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